uu.seUppsala University Publications

Please wait ... |

Link to record
http://uu.diva-portal.org/smash/person.jsf?pid=authority-person:20602 $(function(){PrimeFaces.cw("InputTextarea","widget_formSmash_upper_j_idt129_recordDirectLink",{id:"formSmash:upper:j_idt129:recordDirectLink",widgetVar:"widget_formSmash_upper_j_idt129_recordDirectLink",autoResize:true});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt129_j_idt131",{id:"formSmash:upper:j_idt129:j_idt131",widgetVar:"widget_formSmash_upper_j_idt129_j_idt131",target:"formSmash:upper:j_idt129:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Permanent link

Direct link

Zabzina, Natalia

Open this publication in new window or tab >>Mathematical modelling approach to collective decision-making### Zabzina, Natalia

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_some",{id:"formSmash:j_idt191:0:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_otherAuthors",{id:"formSmash:j_idt191:0:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_otherAuthors",multiple:true}); 2017 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Department of Mathematics, 2017. p. 42
##### Series

Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 99
##### Keywords

collective behaviour, collective decision-making, communication mechanisms, positive feedback, mathematical modelling, bifurcation phenomena, steady state solutions, symmetry breaking, symmetry restoring, diffusion-limited aggregation, fractal dimension
##### National Category

Natural Sciences
##### Identifiers

urn:nbn:se:uu:diva-314903 (URN)978-91-506-2624-7 (ISBN)
##### Public defence

2017-04-07, Siegbahnsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
##### Opponent

### Lundh, Torbjörn

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_j_idt366",{id:"formSmash:j_idt191:0:j_idt195:j_idt366",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_j_idt366",multiple:true});
##### Supervisors

### Gaidashev, Denis

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_j_idt372",{id:"formSmash:j_idt191:0:j_idt195:j_idt372",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_j_idt372",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_j_idt378",{id:"formSmash:j_idt191:0:j_idt195:j_idt378",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_j_idt378",multiple:true});
#####

##### Note

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.

In everyday situations individuals make decisions. For example, a tourist usually chooses a crowded or recommended restaurant to have dinner. Perhaps it is an individual decision, but the observed pattern of decision-making is a collective phenomenon. Collective behaviour emerges from the local interactions that give rise to a complex pattern at the group level. In our example, the recommendations or simple copying the choices of others make a crowded restaurant even more crowded. The rules of interaction between individuals are important to study. Such studies should be complemented by biological experiments. Recent studies of collective phenomena in animal groups help us to understand these rules and develop mathematical models of collective behaviour. The most important communication mechanism is positive feedback between group members, which we observe in our example. In this thesis, we use a generic experimentally validated model of positive feedback to study collective decision-making.

The first part of the thesis is based on the modelling of decision-making associated to the selection of feeding sites. This has been extensively studied for ants and slime moulds. The main contribution of our research is to demonstrate how such aspects as "irrationality", speed and quality of decisions can be modelled using differential equations. We study bifurcation phenomena and describe collective patterns above critical values of a bifurcation points in mathematical and biological terms. In the second part, we demonstrate how the primitive unicellular slime mould *Physarum Polycephalum* provides an easy test-bed for theoretical assumptions and model predictions about decision-making. We study its searching strategies and model decision-making associated to the selection of food options. We also consider the aggregation model to investigate the fractal structure of *Physarum Polycephalum* plasmodia.

Chalmers Tekniska Högskola AB, Göteborg.

Fel serie i tryckt bok /Wrong series in the printed book

Available from: 2017-03-16 Created: 2017-02-07 Last updated: 2017-03-16Open this publication in new window or tab >>A gradient flow approach to the model of positive feedback in decision-making### Zabzina, Natalia

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_some",{id:"formSmash:j_idt191:1:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_otherAuthors",{id:"formSmash:j_idt191:1:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_otherAuthors",multiple:true}); 2015 (English)In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 77, p. 215-224Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Mathematical model of positive feedback in decision making, Gradient flow equations, Differential geometry
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:uu:diva-261246 (URN)10.1016/j.chaos.2015.05.027 (DOI)000358970500022 ()
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_j_idt366",{id:"formSmash:j_idt191:1:j_idt195:j_idt366",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_j_idt366",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_j_idt372",{id:"formSmash:j_idt191:1:j_idt195:j_idt372",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_j_idt372",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_j_idt378",{id:"formSmash:j_idt191:1:j_idt195:j_idt378",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_j_idt378",multiple:true});
#####

Available from: 2015-09-07 Created: 2015-08-31 Last updated: 2017-12-04

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.

Recent studies on social dynamics have been done by using tools and methods of physics and economics.. The main idea is that the regularity observed on a global scale arises out of local interactions between the group members. We consider the model describing one of the major interaction mechanism, the model of positive feedback. We propose a geometrical reformulation of this model in terms of gradient flow equations on a Riemannian manifold. The benefit of this reformulation is that we introduce an alternative method to study phenomena of the well known model. We suggest the analogy with a particle moving on curved manifold. We believe that this analogy will allow us to extend powerful mathematical tools from analytical mechanics to the biological systems.

Open this publication in new window or tab >>Symmetry Restoring Bifurcation in Collective Decision-Making### Zabzina, Natalia

### Dussutour, Audrey

### Mann, Richard P.

### Sumpter, David J. T.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_some",{id:"formSmash:j_idt191:2:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_some",multiple:true}); ### Nicolis, Stamatios C.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_otherAuthors",{id:"formSmash:j_idt191:2:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt191_2_j_idt195_j_idt209",{id:"formSmash:j_idt191:2:j_idt195:j_idt209",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_j_idt209",onLabel:"Hide others...",offLabel:"Show others..."}); 2014 (English)In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 10, no 12, p. e1003960-Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:uu:diva-312747 (URN)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_j_idt366",{id:"formSmash:j_idt191:2:j_idt195:j_idt366",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_j_idt366",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_j_idt372",{id:"formSmash:j_idt191:2:j_idt195:j_idt372",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_j_idt372",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_j_idt378",{id:"formSmash:j_idt191:2:j_idt195:j_idt378",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_j_idt378",multiple:true});
#####

##### Funder

EU, European Research Council, IDCAB 220/104702003
Available from: 2017-01-12 Created: 2017-01-12 Last updated: 2017-11-29

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment.

Open this publication in new window or tab >>Symmetry Restoring Bifurcation in Collective Decision-Making### Zabzina, Natalia

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.### Dussutour, Audrey

### Mann, Richard P.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.### Sumpter, David J. T.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_some",{id:"formSmash:j_idt191:3:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_some",multiple:true}); ### Nicolis, Stamatios C.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_otherAuthors",{id:"formSmash:j_idt191:3:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt191_3_j_idt195_j_idt209",{id:"formSmash:j_idt191:3:j_idt195:j_idt209",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_j_idt209",onLabel:"Hide others...",offLabel:"Show others..."}); 2014 (English)In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 10, no 12, p. e1003960-Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:uu:diva-243062 (URN)10.1371/journal.pcbi.1003960 (DOI)000346656700020 ()
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_j_idt366",{id:"formSmash:j_idt191:3:j_idt195:j_idt366",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_j_idt366",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_j_idt372",{id:"formSmash:j_idt191:3:j_idt195:j_idt372",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_j_idt372",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_j_idt378",{id:"formSmash:j_idt191:3:j_idt195:j_idt378",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_j_idt378",multiple:true});
#####

##### Funder

EU, European Research Council, IDCAB 220/104702003
Available from: 2015-02-09 Created: 2015-02-04 Last updated: 2017-12-04Bibliographically approved

How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment.

Open this publication in new window or tab >>Fractal dimentions of the conformal diffusion-limited aggregation### Gaidashev, Denis

### Zabzina, Natalia

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_some",{id:"formSmash:j_idt191:4:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_otherAuthors",{id:"formSmash:j_idt191:4:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_otherAuthors",multiple:true}); (English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### National Category

Natural Sciences Mathematics
##### Identifiers

urn:nbn:se:uu:diva-314796 (URN)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_j_idt366",{id:"formSmash:j_idt191:4:j_idt195:j_idt366",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_j_idt366",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_j_idt372",{id:"formSmash:j_idt191:4:j_idt195:j_idt372",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_j_idt372",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_j_idt378",{id:"formSmash:j_idt191:4:j_idt195:j_idt378",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_j_idt378",multiple:true});
#####

Available from: 2017-02-06 Created: 2017-02-06 Last updated: 2017-03-01Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.

Diffusion-limited aggregation (DLA) is an important and popular mathematical model of random cluster growth. Conformal DLA, in which a cluster is grown by successive applications of conformal maps, is relletavily new and unexplored version of DLA. We implement conformal DLA numerically and compute several fractal dimentions of DLA clusters. To test applicability of the model to biological systems, the dimentions are compared with the experimentally computed fractal dimentions of the slime mould Physarum Polycephalum.